Control Design And Stability Analysis Of High-order Uncertain Nonlinear Systems With Time-delay

Time-delay phenomena exists in many practical systems such as mechanical, biologicaland economical systems, and the emergence of time-delay is often the signifcant cause ofinstability and the serious deterioration in the system performance, so a number of researcheshave payed careful attention to time-delay systems. Over the past decade, control designproblems for a class of high-order nonlinear system have been one of the hot research areas.the reason is that high-order nonlinear systems contain not only more extensive forms thangeneral feedback nonlinear systems that being extensively studied, on the other hand, italso includes a class of under-actuated, weakly coupled and unstable mechanical systems inpractice. Therefore, it has important theoretical signifcance and actual signifcance to studythe control problems of high-order nonlinear systems.Since the Jacobian linearization of the system at the origin has uncontrollable modesassociated with eigenvalues on the open right-half plane, the traditional method(such asfeedback linearization, backstepping approach) lose efectiveness. Also the study of high-order nonlinear systems become much more difcult with the appearance of time delays.With the method of adding a power integrator, backstepping, fexible adaptive technique, andother techniques such as constructing of Lyapunov-Krasovskii functional and using Young'sinequality, we focus on the two control problems on the global stabilization for a class ofhigh-order time-delay uncertain nonlinear systems:(I) Global stabilization of high-order nonlinear systems with multiple timedelaysThis part investigates the stabilization for a class of high-order nonlinear systems withmultiple time delays. Growth restriction on system nonlinearities is further relaxed. Designprocedures of a continuous controller are provided by the method of adding a power integra-tor, and the stability of the resulting closed-loop system is rigorously proven with the help ofthe elegant choice of a Lyapunov-Krasovskii functional. the controller designed guaranteesthat all the states of the whole closed-loop system are globally uniformly bounded, whilethe original system states globally asymptotically converge to zero. Finally, a simulationexample is provided to demonstrate the validness of the proposed approach.(II) Global adaptive stabilization for a class of high-order time-delay nonlin-ear systems with unknown control coefcients This part investigates the adaptive stabilization for a class of high-order time-delay non-linear systems with unknown control coefcients. Base on the method of adding a powerintegrator, an adaptive stabilizing controller independent of time delays is successfully con-structed by using the backstepping approach and fexible algebra manipulation techniques.it not only guarantees that all states of the whole closed-loop system are globally uniformlybounded, but also makes the original system states globally asymptotically converge to zero.At last, we give a numerical example to demonstrate the efectiveness of the control scheme.Further control problem study of the high-order time-delay nonlinear systems will enrichthe theory of strict feedback nonlinear systems, and will also provide some useful methodsand necessary technique support for the practice.